Question

the length of the hypotenuse, line segment gh, in triangle gjh measures 6 cm. line segment jh measures 2 cm.

Answer 1

The length of the hypotenuse (gh) can be found using the Pythagorean theorem. In this triangle, with gh = 6 cm and jh = 2 cm, we can solve for gj using the theorem. The length of gj is 4√2 cm.

Step-by-step explanation:

The length of the hypotenuse in a right triangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this triangle, the hypotenuse (gh) measures 6 cm and one of the other sides (jh) measures 2 cm. Let's label the remaining side as gj. Using the Pythagorean theorem, we can write:

gh^2 = jh^2 + gj^2

6^2 = 2^2 + gj^2

Simplifying, we get:

36 = 4 + gj^2

Subtracting 4 from both sides, we have:

32 = gj^2

Taking the square root of both sides, we find:

gj = √32 = 4√2 cm

Therefore, the length of gj is 4√2 cm.

Answer 2

Then you can calculate the length of the other segment, gj, using Pytagora's theorem, because when you are talking about hypotenuese you know that it is a right triangle.

hypotenuse^.2 = leg1^2 + leg2^2

(6 cm)^2 = (2 cm)^2 + (segment gj)^2

segment gj^2 = 36 cm^2 - 4cm^2 = 32 cm^2

segment gj =√(32 cm^2) = 5.66 cm